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Measures of Dispersion — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Dispersion4 Marks
Question
Calculate standard deviation and coefficient of variation from the following data with the help of direct method.
S. No. 1 2 3 4 5
Marks 10 12 13 15 20
✓

Answer

Calculation of Standard Deviation and Coefficient of Variation
Marks (X) $X^2$
10 100
12 144
13 169
15 225
20 400
$\Sigma\text{X}=70,\text{n}=5$ $\Sigma\text{X}^2=1,038$
$\bar{\text{X}}=\frac{\Sigma\text{X}}{\text{n}}=\frac{70}{5}=14$
$\sigma=\sqrt{\frac{\Sigma\text{X}^2}{\text{n}}-\Big(\frac{\Sigma\text{X}}{\text{n}}\Big)^2}$
$=\sqrt{\frac{1038}{5}-\Big(\frac{70}{5}\Big)^2}$
$=\sqrt{207.6-196}=\sqrt{11.6}=3.41$
Coefficient of Variation (CV) $=\frac{\sigma}{\bar{\text{X}}}\times100$$=\frac{3.4}{14}\times100=24.35\%$

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